Overview and Abstract

Research Question:

What are indicators of a housing market where homes sell above, below, or at their listed price?

Model Selection:

We ran a full model with Average Sales to List as our response and all other variables of interest as regressors. Looking at the p-values of our output, we found that all variables were statistically significant to our model. After that, we ran a stepwise AIC selection method on our full model which yielded the same results.

Variables:

Average Sales to List: We used this as our response variable. It shows the ratio of asking price to sales price so 100 would mean the house sold for asking price, > 100 means it sold for over asking, and < 100 means it sold for less than asking.

Region: Shows the National average in addition to the six major metro areas that were used in our analysis. The National average was used as the reference.

Days on Market: Median number of days homes sold during the period stayed on the market before going under contract

T10Y: The 10-year US Treasury rate taken on an average monthly basis

M30Y: The Case-Shiller average 30-year fixed mortgage rate

Sold:Inventory Ratio: The ratio of homes sold during a given month compared to the total number of homes on the market

Season: Which season of the month the sales data was recorded in. Winter was used as the reference

Research Question:

Can we predict whether a home will sell within 30 days based on its listing price, number of new listings, inventory, and economic factors in different metro areas?

Summary:

This analysis explores the likelihood of a home selling within 30 days in the Washington, DC metro area using logistic regression. The predictors considered include Median Sales Price, New Listings, Inventory, and the 10-Year Treasury Yield (T10Y). Stepwise and backward model selection indicated that all four predictors should be included in the model, even though Inventory and T10Y were not statistically significant. Assumptions were checked and met.

Interpretation:

• Median Sales Price: The positive coefficient for Median.Sales.Price indicates that higher median sales prices are associated with an increased likelihood of a home selling within 30 days. Specifically, for each additional dollar in the median sales price, the log-odds of a home selling within 30 days increases by 0.0000296. This result is statistically significant (p < 0.01), suggesting a strong relationship between higher prices and quicker sales.

• New Listings: The positive coefficient for New.Listings implies that an increase in the number of new listings is associated with a higher probability of homes selling within 30 days. For each additional new listing, the log-odds of a home selling within 30 days increases by 0.0013742. This predictor is highly significant (p < 0.001), indicating a robust relationship between new listings and the likelihood of quick sales. This may reflect a dynamic market where more new listings attract more buyers quickly.

• Inventory: The coefficient for Inventory is positive but not statistically significant (p > 0.05). This suggests that the total number of homes available for sale does not have a significant direct impact on the likelihood of a home selling within 30 days in this dataset.

• 10-Year Treasury Yield: The positive coefficient for T10Y indicates that higher Treasury yields are associated with an increased likelihood of a home selling within 30 days. However, this predictor is not statistically significant (p > 0.05), suggesting that while there may be a positive relationship, it is not strong enough to be considered significant in this model.

Confusion Matrix and Accuracy:

 Accuracy 
0.8666667 

 Accuracy 
0.8181818 

Area under the curve: 0.9318

Research Question:

Are the number of homes sold in a housing market per month and the average number of days homes sat on the market before going under contract a good measure of how cold, cool, neutral, warm, or hot the market is? (Excluding National figures)

Market Temperature:

Categories created based on the Average Sales to List variable

• Cold: < 95

• Cool: 95-98

• Neutral: 99-101

• Warm: 102-105

• Hot: > 105

Conclusion:

Ultimately, we concluded with training and testing accuracy values of 66.45% and 57.09% that the number of homes sold in a given period and the number of days it sat on the market was not a great predictor of the market temperature

Research Question:

How has the number of homes sold in Washington DC, Philadelphia, and Boston varied on a monthly basis over a six year period between May of 2018 and May of 2024?

Summary:

This analysis investigates the trends in the number of homes sold on a monthly basis from May 2018 to May 2024 in three major metro areas: Washington DC, Philadelphia, and Boston. The LOESS (Locally Estimated Scatterplot Smoothing) method is applied to capture the non-linear patterns in the data, allowing for a detailed understanding of the housing market trends in these regions.

Interpretation:

• Washington DC:

  • The number of homes sold in Washington DC shows noticeable seasonal trends with peaks typically occurring in the spring and summer months. This pattern is consistent with common real estate market cycles where more transactions occur during these periods.

• Philadelphia:

  • Philadelphia exhibits a similar seasonal pattern, with fluctuations in the number of homes sold. The LOESS model captures these trends, showing higher sales volumes in the warmer months and lower volumes in the colder months. Boston:

• Boston:

  • Botson also shows seasonal variations, with peaks in home sales during the spring and summer. The trends captured by the LOESS model reflect the cyclical nature of the housing market in this region.

Research Question:

How does the median home sale price change over time in the DC Metro Area?

Summary

This analysis investigates the changes in median home sale prices over time in the Washington, DC metro area using cubic splines. Cubic splines provide a flexible approach to model non-linear relationships by fitting piecewise polynomials to different segments of the data. The optimal number of knots, which determines the points at which the segments join, was determined using cross-validation to balance model fit and complexity

Research Question:

Can we classify the type of market (buyer’s, seller’s, or equilibrium market) based on economic indicators for different metro areas (Boston, Philadelphia, and Chicago)?

Summary

The Naive Bayes classification model was employed to classify the type of market (buyer’s market, seller’s market, or equilibrium market) based on economic indicators specifically for the Philadelphia metro area. This analysis aimed to determine how well economic indicators can predict market types. The Naive Bayes model was trained using the training dataset (train_dataphilly), with Market.Type as the response variable and Unrate, T10Y, M30Y, and UMCSENT as predictors. These economic indicators were selected based on their potential influence on market conditions.

Interpretation

• Training Accuracy:

  • The model achieved an accuracy of 84.91% on the training dataset. This high accuracy indicates that the model effectively learned the patterns within the training data, correctly classifying the market type in a significant majority of cases.

• Testing Accuracy:

  • The model’s accuracy on the testing dataset was 83.72%. This slightly lower accuracy compared to the training set suggests that the model generalizes well to new, unseen data, maintaining a high level of performance when predicting market types based on economic indicators.

• Model Accuracy:

  • The Naive Bayes model demonstrated strong performance with high accuracy on both training (84.91%) and testing (83.72%) datasets. This indicates the model’s robustness and its ability to generalize well to new data.